A theory of using asymmetric spin echoes is described, in part, in Jensen J. H. et al. Chandra R. Magn Reson Med; 44:144 (2000) (the “Jensen Publication”), the entire disclosure of which is incorporated herein by reference.
The local magnetic field experienced by a water proton is quantitatively characterized by the magnetic field correlation function, K(t), which may be defined byK(|t−t′|)=B(t)B(t′),  [1]with B(t) being the difference, at a time t, between the magnitude of the local field and the magnitude of the spatially uniform main field, B0, and with the angle brackets indicating an averaging over all the water protons within a given region of interest. K(t) may depend on both the spatial distribution of the magnetic field inhomogeneities and the diffusional dynamics of water molecules. The magnetic field correlation function provides information beyond the information contained in the standard nuclear magnetic resonance (“NMR”) relaxation times. Thus, the present invention provides a novel technique to, inter alia, examine the properties of tissue, blood, iron-rich regions of the brain, and tumors.
Although it is believed that the MFC has not been specifically measured, it was introduced at least as early as 1953 in the seminal work of Anderson and Weiss on NMR line shapes. See Anderson P W, Weiss P R, Rev Mod Phys 1953; I25:269-276 (the “Anderson Publication”), the entire disclosure of which is incorporated herein by reference. More recently, it has been utilized in several studies on the modeling of MRI contrast. For example, see Callaghan P T, Oxford University Press, New York, 1991; (the “Callaghan Publication”) Kennan et al., Magn Reson Med 1994; I31:9-21 (the “Kennan Publication”); Stables et al., Magn Reson Med 1998; I40:432-442 (the “Stables Publication”); and the Jensen Publication et al., the entire disclosures of which are incorporated herein by reference.
The MFC may be described as the magnetic resonance (“MR”) signal intensity as a function of the acquisition time, and can be approximated by the exponential form:K(t)=K0exp(−t/τ),  [2]where K0=K(0) is the magnetic field variance and τ is a characteristic decay time. It has recently been shown in the Jensen Publication, that when water diffusion is only weakly restricted the MFC is more accurately described by an algebraic expression of the form:
                              K          ⁡                      (            t            )                          =                                                            K                0                            ⁡                              (                                  1                  +                                      t                    τ                                                  )                                                                    -                3                            /              2                                .                                    [        3        ]            There is not a significant amount of quantitative information regarding the MFC, except for an exact result that can be derived for an idealized random sphere model.
Asymmetric single spin echoes were first introduced by Dixon and Sepponen. In particular, Dixon demonstrated how asymmetric spin echoes can be used to separate the MR signals originating from water and fat. See Dixon W T, Radiology 1984; I153:189-194 (the “Dixon Publication”), the entire disclosure of which is incorporated herein by reference. Sepponen et al., applied asymmetric spin echoes to obtain chemical shift images. See Sepponen R E, et al., Comput. Assist. Tomography 1984; I8:585-587 (the “Sepponen Publication”), the entire disclosure of which is incorporated herein by reference. The asymmetry of the Dixon sequence arises by shifting the signal acquisition time, while the asymmetry of the sequence of Sepponen et al. is achieved by shifting the 180° refocusing pulse.
Asymmetric single spin echo technique with a shifted refocusing pulse has been previously used to obtain MFC data. See Wismer et al., J Comput Assist Tomography 1988; I12:259-265 (the “Wismer Publication”); Rosenthal et al., Invest Radiology 1990; I025:173-178 (the “Rosenthal Publication”); Thulborn et al., Am J Neuroradiol. 1990 (the “Thulborn Publication”); 11:291-297; Hoppel et al., Magn Reson Med 1993; I30:715-723 (the “Hoppel Publication”); Ganesan et al., J. Magn. Reson. (B) 1993; I102:293-298 (the “Ganesan Publication”); and the Stables Publication, the entire disclosures of which are incorporated herein by reference. However, there remains a need for improved methods of measuring the magnetic field correlation.